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1 Survey of utomatc Modulaton Clafcaton Technque: Clacal pproache and New Trend Octava. Dobre, l bd, Yeheel Bar-Ne and We Su 3 Faculty of Engneerng and ppled Scence, Memoral Unverty of Newfoundland St. John, NL B 3X5, Canada Dept. of Electrcal and Computer Engneerng, New Jerey Inttute of Technology, Newar, NJ 7, US 3 US rmy RDECOM Fort Monmouth, NJ, 773, US btract The automatc recognton of the modulaton format of a detected gnal, the ntermedate tep between gnal detecton and demodulaton, a major ta of an ntellgent recever, wth varou cvlan and mltary applcaton. Obvouly, wth no nowledge of the tranmtted data and many unnown parameter at the recever, uch a the gnal power, carrer frequency and phae offet, tmng nformaton, etc., blnd dentfcaton of the modulaton a dffcult ta. Th become even more challengng n real-world cenaro wth multpath fadng, frequency-electve and tme-varyng channel. In th paper we provde a comprehenve urvey of dfferent modulaton recognton technque, n a ytematc way. unfed notaton ued to brng n together, under the ame umbrella, the vat amount of reult and clafer, developed for dfferent modulaton. The two general clae of automatc modulaton dentfcaton algorthm are dcued n detal, whch rely on the lelhood functon and feature of the receved gnal, repectvely. The contrbuton of numerou artcle are ummarzed n compact form. Th help the reader to ee the man charactertc of each technque. However, n many cae, the reported reult n the lterature have been obtaned under dfferent condton. So, we have alo mulated ome major technque under the ame condton, whch allow a far comparon among dfferent methodologe. Furthermore, new problem that have appeared a a reult of emergng wrele technologe are outlned. t the end, open problem and poble drecton for future reearch are brefly dcued. Keyword: utomatc modulaton clafcaton, utomatc modulaton recognton, Clafer performance, Lelhood functon, Maxmum lelhood, Feature extracton, Preproceng ta, Model mmatche, Probablty of correct clafcaton. Part of th wor wa publhed n a prelmnary form and preented at the Sarnoff Sympoum, Prnceton, NJ, US, 8-9 prl 5, under the ttle Blnd modulaton clafcaton: a concept whoe tme ha come.

2 . INTRODUCTION utomatc modulaton clafcaton (MC) an ntermedate tep between gnal detecton and demodulaton, and play a ey role n varou cvlan and mltary applcaton. Implementaton of advanced nformaton ervce and ytem for mltary applcaton, n a crowded electromagnetc pectrum, a challengng ta for communcaton engneer. Frendly gnal hould be ecurely tranmtted and receved, wherea hotle gnal mut be located, dentfed and jammed. The pectrum of thee gnal may range from hgh frequency (HF) to mllmeter frequency band, and ther format can vary from mple narrowband modulaton to wdeband cheme. Under uch condton, advanced technque are requred for real-tme gnal ntercepton and proceng, whch are vtal for decon nvolvng electronc warfare operaton and other tactcal acton. Furthermore, blnd recognton of the modulaton format of the receved gnal an mportant problem n commercal ytem, epecally n oftware defned rado (SDR), whch cope wth the varety of communcaton ytem. Uually, upplementary nformaton tranmtted to reconfgure the SDR ytem. Blnd technque can be ued wth an ntellgent recever, yeldng an ncreae n the tranmon effcency by reducng the overhead. Such applcaton have emerged the need for flexble ntellgent communcaton ytem, where the automatc recognton of the modulaton of a detected gnal a major ta. mplfed bloc dagram of the ytem model hown n Fg.. The degn of a modulaton clafer eentally nvolve two tep: gnal preproceng and proper electon of the clafcaton algorthm. Preproceng ta may nclude, but not lmted to perform ome or all of, noe reducton, etmaton of carrer frequency, ymbol perod, and gnal power, equalzaton, etc. Dependng on the clafcaton algorthm choen n the econd tep, preproceng ta wth dfferent level of accuracy are requred; ome clafcaton method requre prece etmate, wherea other are le entve to the unnown parameter. Regardng the econd tep, two general clae of MC algorthm can be crytallzed, lelhood-baed (LB) []-[6] and feature-baed (FB) [7]-[88] method, repectvely. The former baed on the lelhood functon of the receved gnal and the decon made comparng the lelhood rato agant a threhold. oluton offered by the LB algorthm optmal n the Bayean ene, vz., t mnmze the probablty of fale clafcaton. The optmal oluton uffer from computatonal complexty, whch n many cae of nteret naturally gve re to uboptmal clafer. In the FB approach, on the other hand, everal feature are uually employed and a decon made baed on ther oberved value. Thee feature are normally choen n an ad-hoc way. lthough a FB-baed method may not be optmal, t uually mple to mplement, wth near-optmal performance, when degned properly. Once the modulaton format correctly dentfed, other operaton, uch a gnal demodulaton and nformaton extracton, can be ubequently performed. In general, MC a challengng ta, epecally n a non-cooperatve envronment, where n addton to multpath propagaton, frequency-electvty and tme-varyng nature of the channel, no pror nowledge of the ncomng gnal avalable. In recent year, new technologe for wrele communcaton have emerged. The wrele ndutry ha hown great nteret n orthogonal frequency dvon multplexng (OFDM) ytem, due to the effcency of OFDM cheme to tranmt nformaton n frequency electve fadng channel, wthout complex equalzer

16 phae and frequency of the receved gnal are preented. The econd and thrd part nclude clafer baed on the wavelet tranform and gnal tattc, repectvely. Fnally, a clafer baed on pectral properte of FSK gnal mentoned. In what follow, thee FB-MC algorthm are preented wth a herarchcal approach n mnd,.e., the modulaton cla of the ncomng gnal frt dentfed (e.g., SK, PSK, QM, FSK), and then the modulaton order M wthn the recognzed cla. ngle gnal n WGN, wth the parameter perfectly nown, and a rectangular pule hape u () t were aumed, except otherwe mentoned. In addton to SK, T PSK, QM and FSK, the dentfcaton of other modulaton wa examned n the lterature, e.g., MSK [66], [78]-[8], OQPSK [79], contnuou-phae FSK (CPFSK) [8]. 4.. FB lgorthm to Dtnguh between Dfferent Clae Intantaneou ampltude, phae and frequency-baed algorthm The mot ntutve way to dentfy the modulaton cla of the ncomng gnal to ue the nformaton contaned n t ntantaneou ampltude, phae and frequency. To extract uch nformaton, dfferent method were appled n the lterature [8]-[4]. The followng dfference between gnal clae were employed for clafcaton n [8]-[3]: FSK gnal are characterzed by contant ntantaneou ampltude, wherea SK gnal have ampltude fluctuaton, and PSK gnal have nformaton n the phae. The maxmum of the dcrete Fourer tranform (DFT) of centered 9 normalzed ntantaneou ampltude wa ued a a feature to dtnguh between FSK and SK/ PSK clae, SK and BPSK gnal have no nformaton n the abolute phae, wherea M -PSK ( M > ) ha. The varance of abolute centered 9 normalzed phae wa ued to dtnguh between M -PSK ( M > ) and real-valued contellaton, BPSK and SK, SK gnal have no phae nformaton by ther nature, wherea BPSK ha. Varance of drect (not abolute) centered 9 normalzed phae wa ued to dtnguh between BPSK and SK clae. bnary decon tree tructure wa employed to dcrmnate between clae, and furthermore, wthn each cla, a we wll brefly menton n Secton 4. and 4.3. t each node of the tree, the decon wa made by comparng a tattc agant a threhold 8. In [3] and [33], the varance of the zero-crong nterval wa ued a a feature to dtnguh FSK from PSK and the unmodulated waveform (UW). The zero-crong nterval a meaure of the ntantaneou frequency, and t a tarcae functon for FSK gnal, wherea a contant for UW and PSK gnal. The MC treated a a two hypothe tetng problem: H for FSK and H for UW and PSK. The hypothee are formulated baed on the Gauan aumpton for the etmated feature,.e, N, =,, wth the hypothe-dependent mean ( µ H, σ ) H µ H and varance σ H. n LRT ued for decon, whch due to the Gauan aumpton mplfed to the comparon of the feature agant a threhold η, derved from the LRT. For any two cla problem, aumng equal pror, the average probablty of error then gven by 9 The term centered pecfe that the average removed from the data et. The mean actually the theoretcal value of the feature under H, wherea the varance etmated under each hypothe. 6

18 Intantaneou ampltude and phae-baed algorthm Informaton extracted from the ntantaneou ampltude and phae of the receved gnal wa exploted for lnear modulaton recognton, a follow. The varance of the abolute value of the normalzed centered 9 ntantaneou ampltude wa ued to dtnguh between -SK and 4-SK, a for the former the ampltude change between two level, equal n magntude and oppote n gn, o, t ha no nformaton n the abolute ampltude, wherea t ha for the latter [8]-[3]. The tattc wa compared agant a threhold for decon mang 8 at a tree node, a part of the bnary decon tree clafer mentoned n Secton 4.. The phae PDF and t tattcal moment were nvetgated for PSK gnal recognton n [44]-[5]. The phae PDF multmodal, and the number of mode provde nformaton for the PSK order dentfcaton. In the hgh-snr regon, M -PSK exbt M dtnct mode, whle when the SNR decreae or M ncreae, the pea mear off and fnally the PDF converge to a unform PDF [48]. Specfcally for PSK gnal clafcaton, an approxmaton ung the Tchonov PDF and a Fourer ere expanon of the phae PDF were employed n [44]-[46], wth a loglelhood rato tet for decon. By ung thee method to compute the phae PDF, cloed-form expreon for the phae tattcal moment were derved, and the PDF of the ample etmate of the moment were ued for decon mang [47]-[5]. The dtrbuton of the ample etmate of the n th-order moment wa aumed to be Gauan, ( µ, σ ) N nh, nh,, where the mean nh, µ and varance σ nh, depend on the hypothe H and n. The decon crteron wa further reduced to comparng the ample etmate of the phae moment wth a threhold. The htogram of the phae dfference between two adjacent ymbol wa ued n [3], [33], [39] for PSK order dentfcaton, wth the decon made baed on the comparon of the htogram agant partcular pattern. The perodc component of the phae PDF were analyzed for PSK order dentfcaton n [5], ung the DFT of the phae htogram. In other word, the emprcal charactertc functon of the phae wa exploted for clafcaton n th wor. Furthermore, n [5] the algorthm wa extended to QM gnal clafcaton, by explotng the addtonal nformaton provded by the magntude of the receved gnal. Other feature extracted from the ntantaneou ampltude and phae were nvetgated for PSK and QM dentfcaton n [4], [78], [83], [84], uch a the urto of the ampltude. Wavelet tranform-baed algorthm Dfferent PSK gnal gve re to dfferent et of pea value n the magntude of the Haar wavelet tranform. The htogram of the pea magntude wa employed to dentfy the order of a PSK gnal n [37], wth the decon made by comparng the htogram wth the theoretcal PDF correpondng to dfferent order. Sgnal tattc-baed algorthm Cumulant-baed feature were propoed n [4] to dentfy the order of SK, PSK, and QM modulaton, a follow: the normalzed cumulant of fourth-order/ two-conjugate, c ( )/ c (), for SK, the magntude of r,4, 3 r,, the normalzed cumulant of fourth-order/zero-conjugate, c ( )/ c (), for PSK ( M > ), and the normalzed r,4, 3 r,, cumulant of fourth-order/zero-conjugate, c ( )/ c (), for QM. The theoretcal value of the n th-order/ r,4, 3 r,, q -conjugate cumulant c, ( q =,..., n /, n even, for everal lnear modulaton are gven n Table IV. Thee ),, nq 8

19 value were computed ung the moment to cumulant formula 6, n whch the nth-order moment were calculated a enemble average over the noe-free unt-varance contellaton wth equprobable ymbol. Note that due to the ymmetry of the gnal contellaton condered, the nth-order moment for n odd are zero and hence, ung the moment to cumulant formula, t eay to how that the nth-order cumulant for n odd are alo zero. On the other hand, for n even we have c () = c (). n LRT wa formulated baed on the PDF of the ample etmate of, nq,, nn, q feature, whch are Gauan,.e., N ( µ H, σ ) H. Wth a mplfyng approxmaton,.e., equal varance under all the hypothee, the decon wa further reduced to comparng the ample etmate of the choen feature ˆω agant a threhold, wth ω a any of the cumulant-baed feature prevouly mentoned. For an N mod hypothe tetng problem, wth the hypothee ordered uch that µ H <µ... H < <µ H N, the decon rule to chooe H f mod ( µ +µ )/ <ω< ˆ ( µ +µ )/, (3) H H H H+ where µ H = and µ =. H N mod + Note that the cumulant-baed feature c ( )/ c () and r,4, 3 r,, c ( )/ c () do not depend on a fxed carrer r,4, 3 r,, phae θ, a for q = n/ the exponental factor whch depend on θ cancel each other, wherea for q n/ the phae dependency dropped by tang the magntude. Th wor wa extended n [53] to clafy lnear modulaton n frequency-electve channel. The blnd alphabet-matched equalzaton algorthm (M) [], whch wa ued for equalzaton, wa alo employed for clafcaton. Some other cumulant-baed feature were added [3] to the et of feature extracted from the ntantaneou ampltude, phae and frequency [8]-[9], to nclude QM gnal n the et of canddate modulaton to be recognzed. Sgnal moment were appled to dtnguh between QPSK and 6-QM n [54]. Specfcally, a lnear combnaton of the fourth-order/two-conjugate moment and the quared econd-order/one-conjugate moment were employed, wth the coeffcent and the delay vector optmzed to maxmze the probablty of correct clafcaton. et of feature wa choen for certan value of the delay vector, and clafcaton wa made baed on the correlaton between the ample etmate and theoretcal feature vector. The gnal-moment feature m ( )/ m () wa employed to dentfy the order of QM gnal n [4], wth the decon made baed on 3 r,6,3 5 r,, the mnmum abolute value of the dfference between the ample etmate and precrbed value of the feature. Sgnal cyclotatonarty wa alo exploted for lnear modulaton dentfcaton [55]-[65], va two approache: pectral lne generaton when pang the gnal through dfferent nonlnearte [55]-[57], and perodc fluctuaton wth tme of cumulant up to the n th-order [58]-[65]. We note that the n th-order cycle frequence (CF) are gven by ( n q) f + m/ T, wth m an nteger [6], [63]. The n th-order CF formula alo hold for an IF gnal, where f replaced by the IF frequency, f IF. Wth th property, the cyclotatonarty of the receved gnal wa exploted for MC through a pattern of ne-wave frequence n gnal polynomal tranformaton. For example, the f IF and 4 f IF nuod that appear n the econd and fourth power of the receved gnal, repectvely, were ued n [55] to dtnguh between BPSK and QPSK. In [56], [57] the ame property wa 9

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